Can anyone explain to me why 準備が出来ている means "It's ready?" I don't think I know exactly what 出来ます means, as we initially learned it as "able to"- but I've seen other uses like in saying "I have/got a girlfriend," or "There is a library." (At least, I think the latter, like 図書館が出来た." In any event, I know 準備 is preparation, so the real question is what does 出来ている mean, and why does it mean that?
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There are two uses of できる:
出来る (usually written in kana) can take on several different meanings (see e.g. http://tangorin.com/general/出来る for the entire list). Here it means that the preparations "became finished".
In the sentence "図書館ができた", it means that a library was built.